A Method for the Analysis of Transient Motion of a Kelvin-Voigt Half-Space

Abstract

ABSTRACTIn this paper, a modified version of method of steepest descent combining with Durbin's method is proposed to study the transient motion in either an elastic or a viscoelastic half-space. The causal condition is satisfied based on the Durbin's method while the wavenumber integral for any range of frequency is evaluated by applying the modified method of steepest descent. The validity and accuracy of the proposed method is tested by studying the transient response generated by a buried dilatational line source in an elastic half-space, for which the exact solution (Garvin's solution) can be obtained. Then the same formalism is extended to Kelvin-Voigt half-space, and the transient surface motions in elastic or viscoelastic half-spaces media are studied and discussed in details.